Distributed Sensing and Shape Control of Piezoelectric Bimorph Mirrors

Abstract

Abstract As part of a collaborative effort between Sandia National Laboratories and the University of Kentucky to develop a deployable mirror for remote sensing applications, research in shape sensing and control algorithms that leverage the distributed nature of electron gun excitation for piezoelectric bimorph mirrors is summarized. A coarse shape sensing technique is developed that uses reflected light rays from the sample surface to provide discrete slope measurements. Estimates of surface profiles are obtained with a cubic spline curve fitting algorithm. Experiments on a PZT bimorph illustrate appropriate deformation trends as a function of excitation voltage. A parallel effort to effect desired shape changes through electron gun excitation is also summarized. A one dimensional model-based algorithm is developed to correct profile errors in bimorph beams. A more useful two dimensional algorithm is also developed that relies on measured voltage-curvature sensitivities to provide corrective excitation profiles for the top and bottom surfaces of bimorph plates. The two algorithms are illustrated using finite element models of PZT bimorph structures subjected to arbitrary disturbances. Corrective excitation profiles that yield desired parabolic forms are computed, and are shown to provide the necessary corrective action.